How to solve this Q?

[Gee]

Half the pieces of chalk in a box were white, the rest were coloured. A third of
the coloured ones were blue, a quarter of the rest were red and the others
were yellow. If there are 6 yellow ones, how many pieces of chalk were there
altogether.

Looks simple but the sum doesn't make sense. I may interpret 'a quarter of teh rest were red' wrongly.

Please help.

Thanks.

[Guest55]

Half the pieces of chalk in a box were white, the rest were coloured. A third of the coloured ones were blue, a quarter of the rest were red and the others were yellow. If there are 6 yellow ones, how many pieces of chalk were there altogether.

We know there are 6 yellow.
Half are coloured - third of these are blue so 1/6 blue.
The others are red and yellow; these are [1 - (1/2 + 1/6)] = 1/3
So if 1/4 of these are red 3/4 of this 1/3 are yellow ie 1/4 are yellow, so there are 24 altogether.

CHECK: 12 white, 12 coloured [4 blue, 2 red, 6 yellow]

[Gee]

Half the pieces of chalk in a box were white, the rest were coloured. A third of the coloured ones were blue, a quarter of the rest were red and the others were yellow. If there are 6 yellow ones, how many pieces of chalk were there altogether.

We know there are 6 yellow.
Half are coloured - third of these are blue so 1/6 blue.
The others are red and yellow; these are [1 - (1/2 + 1/6)] = 1/3
So if 1/4 of these are red 3/4 of this 1/3 are yellow ie 1/4 are yellow, so there are 24 altogether.

CHECK: 12 white, 12 coloured [4 blue, 2 red, 6 yellow]

Thank you so much for the quick reply. Very well explained.